Quantum corrections to generic branes: DBI, NLSM, and more

We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

A canonical analysis of the massless superparticle

The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor θ present; no attempt is made to maintain manifest covariance. Upon using the Dirac bracket to eliminate the second class constraints arising from the canonical momenta associated with half of these components, we find that the remaining components have canonical momenta that are all first-class constraints. From these first class constraints, it is possible to derive the generator of half of the local Fermionic κ-symmetry of Siegel; which half is contingent upon the choice of which half of the momenta associated with the components of θ are taken to be second class constraints. The algebra of the generator of this Fermionic symmetry transformation is examined.

COUPLING CHIRAL BOSONS TO GRAVITY

The chiral boson actions of Floreanini and Jackiw (FJ), and of McClain, Wu and Yu (MWY) have recently been shown to be different representations of the same chiral boson theory. MWY displays manifest covariance and also a (gauge) symmetry that is hidden in the FJ side, which, on the other hand, displays the physical spectrum in a simpler manner. We make use of the manifest covariance of the MWY chiral boson representation to couple it to background gravity showing explicitly the equivalence with the previous results for the FJ representation.

ON MANIFEST COVARIANCE CONDITION IN THE LAGRANGIAN FORMALISM

The manifest covariance condition for a Poincaré covariant theory is analyzed in the framework of the Lagrangian formalism in a systematic way. We prove that this result is of a kinematic nature and also show that in some cases one needs an appropriate generalization of the Lagrangian formalism. Then the manifest covariance condition is analyzed in a Galilei invariant theory, obtaining the most general type of interaction allowed by this condition.

MANIFEST COVARIANCE CONDITION IN THE HAMILTONIAN THEORY OF RELATIVISTIC STRINGS

The manifest covariance condition of Currie, Jordan and Sudarshan is generalized in a natural manner to the theory of one relativistic string. Then, all “local” solutions of a certain type (suggested by the existing literature) are classified. It is not clear if one of them corresponds to the usual string theory based on the Nambu-Goto Lagrangian. The analysis is performed in the framework of the Hamiltonian formalism.

MANIFEST COVARIANCE CONDITION IN A RELATIVISTIC LAGRANGIAN STRING THEORY

The manifest covariance condition of Currie and Hill for a relativistic Lagrangian N-particle theory is generalized for a Lagrangian relativistic string theory. The corresponding Currie–Hill equations are derived. We can analyze the emerging problem only in a particular case, and we obtain only a trivial solution for the Lagrangian. This seems to indicate that a non-constrained Lagrangian formalism is not very suitable for the description of a relativistic string.

A quantization of the electromagnetic field

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.